Atoms in coherent and incoherent fields: I. Microscopic theory of Einstein's rate equation

Abstract

A fundamental investigation of the problem of an incoherently driven two-level atom is presented. In the case of a black body (thermal) broad band field the Einstein radiation rate equation is derived once a statistical decorrelation between matter and field variables is made. This is also shown to be true for N #62; 1 independent (non-cooperative) atoms. The normalised second order correlation function g (2)(0) = 2 for N ⪢ 1, characterising the chaotic nature of the scattered field. We also investigate the hierarchy of approximations to the rate equation. To first order in the coupling constant e 2 ( e is the electron charge) a generalised (correlated) rate equation, for a single atom, is derived. The statistical correlation of field and matter has its effect on the atomic saturation as well as on the scattered radiation where g (2)(∞) #62; 1 (partial coherence) compared with full coherent radiation, g (2)(∞) = 1, in the decorrelated case.